|
| |
|
|
A052841
|
|
A simple grammar.
|
|
9
| |
|
|
1, 0, 2, 6, 38, 270, 2342, 23646, 272918, 3543630, 51123782, 811316286, 14045783798, 263429174190, 5320671485222, 115141595488926, 2657827340990678, 65185383514567950, 1692767331628422662
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Stirling transform of A005359(n)=[0,2,0,24,0,720,...] is a(n)=[0,2,6,38,270,...]. - Michael Somos Mar 04 2004
Stirling transform of -(-1)^n*A052657(n-1)=[0,0,2,-6,48,-240,...] is a(n-1)=[0,0,2,6,38,270,...]. - Michael Somos Mar 04 2004
Stirling transform of -(-1)^n*A052558(n-1)=[1,-1,4,-12,72,-360,...] is a(n-1)=[1,0,2,6,38,270,...]. - Michael Somos Mar 04 2004
Stirling transform of 2*A052591(n)=[2,4,24,96,...] is a(n+1)=[2,6,38,270,...]. - Michael Somos Mar 04 2004
|
|
|
LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 808
C. G. Bower, Transforms (2)
|
|
|
FORMULA
| E.g.f.: 1/(exp(x)*(2-exp(x))).
O.g.f.: Sum_{n>=0} (2*n)! * x^(2*n) / Product_{k=1..2*n} (1-k*x). [From Paul D. Hanna, Jul 20 2011]
a( n) = (A000670(n) + (-1)^n)/2 = Sum_{k>=0} (k-1)^n/2^(k+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 02 2003
Also, a(n) = Sum[k=0..[n/2], (2k)!*Stirling2(n, 2k)]. - R. Stephan, May 23 2004
a(n) = D^n(1/(1-x^2)) evaluated at x = 0, where D is the operator (1+x)*d/dx. Cf. A000670 and A005649. - Peter Bala, Nov 25 2011
|
|
|
MAPLE
| spec := [S, {B=Prod(C, C), C=Set(Z, 1 <= card), S=Sequence(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, n!*polcoeff(subst(1/(1-y^2), y, exp(x+x*O(x^n))-1), n))
(PARI) {a(n)=polcoeff(sum(m=0, n, (2*m)!*x^(2*m)/prod(k=1, 2*m, 1-k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */
|
|
|
CROSSREFS
| Inverse binomial transform of A000670.
Sequence in context: A027322 A085447 A078673 * A197972 A068184 A067106
Adjacent sequences: A052838 A052839 A052840 * A052842 A052843 A052844
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
| |
|
|
